Algebraic and Arithmetic Geometry Seminar

Constructing $T$-singular surfaces

by Julie Rana (Lawrence University)

Aula Magna (Dipartimento di Matematica)

Aula Magna

Dipartimento di Matematica


Semi-log-canonical surfaces with ample canonical divisors are called stable. Their moduli space is a natural compactification (the KSBA compactification) of the Gieseker moduli space of canonical models of surfaces of general type. Among the singularities that are allowed in stable surfaces, we have cyclic quotient singularities $1/m(1; q)$, and a special role is played by those with $m =dn^2$, $q=dna-1$ $\mathsf{gcd}(n; a) = 1$. These singularities together with all du Val singularities are called T-singularities. We give bounds on such singularities and describe some constructions.